Preface to Being and Time, Martin Heidegger summarizes the aim of
the investigation upon which he and the reader are about to embark – an
investigation Heidegger himself never completed – as “the Interpretation
of time as the possible horizon for any understanding whatsoever
His first English translators, John Macquarrie and Edward Robinson,
immediately warn the English-speaking reader in a note that for
Heidegger the word “horizon” has meanings they will find unfamiliar. “We
tend to think”, they write, “of a horizon as something which we may
widen or extend or go beyond; Heidegger, however, seems to think of it
as something which we can neither widen nor go beyond, but which
provides the limits for certain intellectual activities performed
Time, we might rephrase Heidegger to say, is the one condition – the
horizon – beyond which we cannot go, under which the question of Being
must inevitably and always be asked.
Phenomenology has been out of style for some time, but the
phenomenological metaphor of the “horizon” has persisted, perhaps
entering present critical and hermeneutic discussion most directly
through the writing of Heidegger’s student, Hans-Georg Gadamer, who in
his Truth and Method connects this metaphor not so much with
explicit ontology as with the temporality, and more specifically, with
the cultural historicity, of the individual subject. Following Gadamer,
it became common to speak of activities of interpretation, from
encountering people unlike ourselves, or other people taken altogether,
to the reading of literature or the viewing of art, as a “fusion of
That is, to return to the explanation of Macquarrie and Robinson, the
limits of the intellectual activities, the “prejudices” in the neutral
sense in which Gadamer meant us to use that otherwise charged term, must
reach an accommodation, or fusion, with other such limits.
Whether we think of horizons as limits of thought, as culturally
specific assumptions or “prejudices” about the “world” in which we
happen to live – and of course “world” in this metaphorical sense is
closely related to “horizon” – or as limits of experience in some way or
another to be extended or exceeded, the horizon metaphor entails limits
and boundaries. What are these limits and boundaries? Probably the most
common meaning of “horizon” is the apparent meeting of earth and sky,
but when we speak, for example, of “opening up new horizons” we mean
more than that. We mean entering a new sphere of experience, and even in
this case the horizon so to speak exists around us, or between us
and the juncture of earth and sky. It is also important that; although
there may be “clouds on the horizon”, the “horizon” metaphor, either as
the limit of the most authentic thinking, or as a limit constantly to
the extended, is positive, and the limit it implies is a definition
relative to which these fundamental human activities may be carried out.
However we might spin out these examples, “horizon” remains close to its
etymological roots. The word descends more or less directly from the
Greek. The verb horizein means to mark out by boundaries, lay
down, limit or define. It may also mean to mark out for oneself, to set
up or dedicate, to determine, appoint of settle. The noun is horos,
which may refer to mountains or hills, but also to boundaries,
limits, frontiers and borders, especially those defined by a landmark.
Horoi were also inscribed stones set up to mark mortgaged
property. More metaphorically, horoi might be any rule, standard,
limit or measure, or finally, the definition of a word.
“Horizon” is thus an excellent example of what I call a “real spatial
a metaphor that takes its value from our embodied experience of the
world in which we find ourselves, and at its etymological base it
belongs with such other metaphors as “precinct” (from praecingere,
to belt or girdle), templum, temenos, and a great many words
in a great many languages of which I am unaware that refer to limits and
boundaries, words, that is, that refer to qualitative differences
between inside and outside.
The limits and boundaries implied by horizon and related terms are
essentially arbitrary, and so in need of some additional warrant
or sanction. If horos may refer to a hill or mountain, that hill
or mountain has entirely different meanings if it marks the boundary of
a sacred precinct, the border of a nation, or the extent of property. To
put this in other terms, the specific forms in which limits and
boundaries are encountered, respected, and negotiated always represent
cultural choices. It is important to distinguish limits and boundaries
as conditions of human social life from those results of cultural
choices, the specific limits and boundaries, inclusions and exclusions,
understood by members of specific human groups. But if the etymology of
horizon leads us to Greek social spaces and their markers, how did
“horizon” come to refer to what we call “horizons”? If a horizon is
a limit, and might in principle be the walls of a city or the
precinct of a temple, why do we reserve the horizon metaphor for the
limits of vision? Why is the horizon metaphor so closely associated with
perspective, or better, with the modern perspective metaphor? And how
did both of these words become so closely associated with the “subject”,
and at the same time with “world” and “culture”?
In order to begin to address these questions, and to bring the horizon
metaphor into clearer focus, we must inquire after a further essential
element. We do not think of horizons as real limits but rather as
literally pro-visional limits established in relation to a
center, a consciousness, ourselves, for example, for whom the limit is a
limit of vision. In itself, this limit may shift, and indeed
is constantly shifting; but the center relative to which the limit
both shifts and remains the same persists, at least for a time, until
that center is no more. The horizon is thus defined as and by the
ongoing and cumulative experience of a subject. Where did this
conception of center and limit come from?
Once again, it came from the Greeks. Aristotle was probably not the
first to observe, as he does in his Meteorology, that “throughout
the habitable world the horizon constantly shifts, which indicates that
we live on the convex surface of sphere”.
This statement occurs in the midst of arguments brushing aside the
belief of Anaxagoras that the earth is a disk, which Aristotle thought
was preposterous. The earth, he argued instead, is a sphere, and he does
not mean that all horizons “constantly shift” because there are
mountains here and plains or oceans there, but rather that, wherever the
center of ourselves may go, the world is always dropping out of sight at
the edges. If the earth were a perfect sphere, and air perfectly clear,
then the horizon, the limit of the field of vision, would be the same
in any direction we turned, and, because of the curvature of the earth,
it would drop out of sight in all directions at the same distance, thus
forming a circle around the center, the seeing subject. Not
incidentally, sight might thus measure sections of the earth’s convex
surface and its volume.
Toward the end of the Classical tradition, late in the fourth century C.
E., Macrobius wrote that wherever you stand, you will seem to see an end
to the heavens, and the ancients – perhaps Aristotle by this time –
called this the “horizon”.
Macrobius expanded these remarks in his Commentary on the Dream of
Scipio, writing that there are ten circles in the cosmos after the
Milky Way. These include the zodiac and the ecliptic, plus five circles
on the earth’s surface, the polar circles, the tropics and the equator.
The final two circles are the meridian and the horizon (Stahl, p. 152),
which he says, are not inscribed on the sphere, because they have no
fixed place. Because the earth is round, the sun is directly overhead,
or it is noon, only in one place at one time. “Similarly”, Macrobius
continues, “the circumspection [in the literal sense of looking all
around in a circle] of individuals (singulorum) makes a horizon
for [each of] them. The horizon is a circular boundary that marks the
apparent junction of the sky and the earth, and since our eyes cannot
see to the ends of the earth, as much as each one beholds by looking
about him in all directions is for him his individual boundary of that
portion of the sky above the earth. This horizon, which each one’s
vision circumscribes for himself, cannot extend beyond three hundred and
sixty stades in diameter [about 35 miles], for vision does not exceed
180 stades in any one direction. When it reaches this point [vision]
fails since what is beyond is concealed from us by the roundness of the
earth”. These limits continue as the observer moves, and are once again
to be realized only under conditions of near-perfect sphericity, “ on a
perfectly flat plain, or at sea in a moment of tranquility”.
Macrobius did not distinguish, as astronomical writers did, between this
“sensible” horizon and the “rational” horizon, the second a plane
through the center of the earth, perpendicular to the position of the
viewer on the earth’s surface, relative to which the varying visibility
of the fixed stars could be plotted. Such abbreviations notwithstanding,
however, the examples of Aristotle and Macrobius are sufficient to
explain why in ancient writers the word horizon often appears
with the word kyklos, circle, and, since a circle may be
completed as a sphere, why horizon also appears with aer.
Macrobius seems to be imagining that each of us has a kind of
hemispheric bubble of atmosphere, the circumference of the base of
which, and the vertical radius of which, is defined by the limits of
A certain number of tentative conclusions may be offered. First, what
must have been the older real spatial definition of horizon as a
boundary was expanded to entirely new levels of scale and abstraction as
part of Greek natural philosophy, and, more specifically, of cosmography
and cosmology. In this expansion, the term retained its precinct-like
connotations of qualitative inside and outside, that which is inside
being the province of individual experience as delimited by sight. In
addition, the horizon circle located human awareness within the embrace
of the great circles of the cosmos itself. It also vividly characterized
the uniqueness of the physical conditions of human consciousness, giving
equally unique dimension to the perennial classical theme of human
(Animals have no horizons because they are always looking down.) In this
scheme, sight itself is subject to geometric description and under ideal
conditions is a precise measuring device.
At the same time that it had a more or less stable geometry, reflecting
a higher, absolutely stable geometry, the horizon circle also had a
radically temporal center, the experiencing (if interchangeable)
individual, upon whom it was dependent in the sense that, as the
individual moved, the circle also moved, even if the circle always
remained the same.
The horizon circle located human experience in the harmony of the
circles of the world at large, but it also absolutely associated the
microcosm of human awareness, not just with vision, but with optics,
that is, with the – once again culturally specific – geometric
description and explanation of vision. Although it is a related
geometry, optics raises new issues. When we look at the horizon – when
we watch the sun set, for example – we say that the earth at our feet
“rises” to the horizon, to the meeting of earth and sky. When we say
that, we mean that the earth’s measurable surface on which we stand is
the base of a very acute angle, and that along this base measures are
seen under smaller and smaller visual angles, rising to the height of
our point of view, and of our line of sight, as it meets the horizon. In
principle, if the world were a perfect plane, this diminution might go
on indefinitely, but according to the argument I am following, it must
stop at a certain point because, even though the world is a very large
sphere, and looks flat from wherever we might be, it eventually curves
away out of sight. In effect, the line of sight becomes tangent to the
earth’s sphere as the plane of the earth and the parallel line of sight
come together at the horizon.
I will return to the question of the connection of the horizon circle
and optics, but first I want briefly to outline the history of the
horizon circle in Europe after antiquity. Macrobius was a major source
for medieval encyclopedists, but it was only in the 13th century, well
into the project of the reclamation of classical science, that the
ancient terms and definitions began to reappear. Astronomy itself is
key. John of Sacrobosco’s De sphaera mundi, which would remain a
basic university textbook through the Renaissance, was circulating by
In a French introduction to astronomy written around 1250 we read that
the horizon is “a circular line where the earth seems to rejoin the
By the time Dante wrote the Divine Comedy, the cosmic geometry of
revived astronomy provided a firm armature for his imagination. Here is
the beginning of Canto II of the Purgatory.“The sun had now
reached the horizon whose meridian circle covers Jerusalem with its
highest point”. That is, the sun, standing directly over Jerusalem, in
the east, appeared to be just rising from where Dante stood. The term is
encountered more and more frequently in European writers through the
14th century. “Horizon” could also take more pictorial forms, perhaps
paralleling the rise of landscape. Around 1375 Geoffrey Chaucer (who
wrote a treatise on the astrolabe) described the break of dawn as
follows: “And whiten gan the orisonte shene”.
In the later 15th century, Lorenzo de’ Medici, converted the definition
of “horizon” – "nothing else than the last limit, beyond which human eyes
– into a meditation on the western horizon of death, about which the
sunflower instructs us by turning her last loving gaze to the sun’s
disappearance. The center that defines the circle perishes. When he
describes the horizon as “that last place where the setting sun is no
longer seen, and, when it rises, the first place the sun appears”,
Lorenzo might have been imagining the classical circle and the curvature
of the world, or the possibly endlessly planar extent of then-new
one-point perspective construction. Leonardo da Vinci certainly meant to
refer to perspective construction when he advised the painter not to put
“histories” one above the other on the same wall, because their
different horizons would look like a bottega di merciaio with all
of its little square boxes.
In the 13th century Thomas Aquinas gave a new metaphorical meaning to
“horizon” that would be elaborated by Neoplatonic writers like Marsilio
Ficino and Giovanni Pico della Mirandola. Aquinas began from the
astronomical definition – “horizon is the circle where vision
terminates, the lower limit of the hemisphere above and the beginning of
the hemisphere below;” and as similar unions of heaven and earth, of
soul and body, human beings may properly be called “horizons”. “The
intellectual soul [that is, the uniquely human soul, as opposed to
vegetable and animal souls] is said to be as if a certain horizon and
confinium [a common border] of the corporeal and the incorporeal,
insofar as its substance [essential nature] is incorporeal, although it
is corporeal in the form of a body.” The virtual meeting of earth
and sky is the condition of humanity in statu viae, on the way
through the pilgrimage of this life.
If in the very long tradition I have outlined the horizon is a circle,
how did it become a straight line, a horizontal line? In ancient
writers, sufficient reality seems to have been given to the horizon
circle by the confidence that, under ideal circumstances, sight would
measure a perfect circle from a single point of view. The concentricity
of this ideal circle with the larger order must also have bolstered this
confidence. But however we might think about them, the representation
of apparent horizons is only possible in virtual space, more
particularly, in painting, and the words of Chaucer, Lorenzo de’Medici,
and Leonardo da Vinci suggest that painting was an important factor in
the transformation from the curved horizon to the straight. To be sure,
if we are standing at the center of a circle 35 miles in diameter, the
edge of the circle – 17.5 miles away at any point – will appear to be
nearly straight. But strictly speaking it is not straight, and in order
to understand a crucial – and ongoing – episode in the historical life
of the horizon metaphor, we must return to the connection between the
horizon circle and optics.
As I have mentioned, classical optics was based on the principle that
light travels in straight lines, and that vision could therefore be
described geometrically as the relation of straight lines to a point, a
“point of view”, as we still say, which might coincide with the point at
the center of the horizon circle, connected by the line of sight to a
point on the horizon circle. The economy of light or sight with respect
to a point provided the basic analytical tool of optics, the visual
angle, which, as I have also briefly mentioned, made it possible to
explain why equal quantities appear to be unequal at different
distances, why, for example, the columns in a colonnade appear to
recede: from the same point each column is seen under a smaller and
smaller visual angle. And so all kinds of visual appearances might be
explained, why, for example, circles appear to be ovals when not seen
straight on, and, to return to my earlier discussion, why the ground
beneath our feet appears to rise to the horizon.
Although both cosmography and optics were disciplines to which geometric
demonstrations were indispensable, optics was by and large not concerned
with problems of curvature. The base of the visual angle of optics was a
line standing for a quantity, and, if this line was expanded into a
second dimension, the shape was a square or circle at the base of a
three-dimensional pyramid or cone. I have argued elsewhere that the
beginnings of Greek optics coincided closely with the invention of
architectural scene-painting for tragic theater by the painter
Agatharcus of Samos in Athens in the second half of the 5th century B.
A virtual stage of space was literally fundamental to this fictive
architecture, and, because it was lower by construction than the point
and line of sight, it appeared to rise with distance. This is an
optic plane, and whether or not a whole architectural illusion was
constructed, it was possible to make the appearance of a virtual stage
of space simply by drawing a horizontal line across the surface, a
device that has survived to the present.
When ancient scene-painting and architectural drawing – to both of which
Vitruvius gave the same name, skenographia – were re-invented in
the optic plane became modular, Leon Battista Alberti’s famous
checkerboard. In an Albertian perspective construction the last thing to
be drawn is the horizon, which Alberti did not call a horizon. (Although
a disk he called a horizon was part of the apparatus he set out in his
treatise on sculpture.) Having projected his gridded optic plane, with
its recessive diagonals obedient to the centric point and line of sight,
Alberti drew a horizontal line through this “centric point”. “When I
have carefully done these things, I draw a line across, equidistant from
the other lines below [that is, parallel to the transversal lines
defining the grid below] , which cuts the two upright sides of the large
rectangle [that is, his “window”, or panel] and passes through the
centric point. This line is for me a limit or boundary [terminus
atque limes], which no quantity exceeds that is not higher
than the eye of the spectator. Since it passes through the centric
point, this line may be called the centric line”.
Alberti’s centric line is defined in terms like those used for the
horizon, but he says that it is a limit in that only things taller than
a human being – trees, mountains, buildings – may be placed above it.
More generally, however, reference of this limit to the center implies
that the view framed by the panel is a segment of the horizon for a
viewer. But there are fundamental differences between Alberti and
Alberti’s construction defines only a pencil of space, a tunnel of
ratios, so to speak, derived from the modular division of the baseline
of the painting. The entire framework of his construction is parallel to
that baseline. Since it extends “almost to infinity” [paene usque ad
the tunnel cannot acknowledge the curvature of the earth, which by
implication becomes endlessly planar, perfectly and notionally flat. Nor
can the horizon line acknowledge the horizon circle, because it is
“almost at an infinite distance” beyond the limits of vision. Even if we
think of a much greater horizon circle, Alberti’s centric line,
determined by the baseline and its modular division, must be tangent to
this greater circle, and so assumes an independence from any possible
limit of human vision, thus to constitute an infinity.
This infinity – not only in depth, since the horizon line might also be
extended endlessly to either side – comes into view only when the
geometry of vision is developed as if it were pure geometry. Then the
straight line of the horizon implies the separation of the geometry of
space from the geometry of vision, what I have called metaopticality.
This separation is entirely consistent with the emergence of an
important modern definition of objectivity, achieved by removing the
visual angle from the metaoptical matrix, thus to yield the infinite
coordinate framework of classical Newtonian physics, which although
supplanted, remains the framework of the control and prediction of force
basic to modern technological life. Since metaoptical space
universalizes the principle of modularity – it is isometric, even if the
unit of measure is arbitrary – and static, it is perhaps understandable
that perspective, at least from Henri Bergson onward, has been
associated with instrumental reason, and opposed to a deeper life
principle, thus to become one of the prime villains of contemporary
Things, however, are not so simple, and perhaps not so bad. When Alberti
wrote his treatise on painting, even though he wished to make painting
an intellectual and liberal art by associating it with geometry, he
reined in his Euclidean impulses a bit when he wrote that his parallel
lines recede “almost to infinity”. In general, Alberti wrote of
pursuing “ a plumper Minerva”,
a plumper wisdom, and he claimed to be writing as a painter. In these
terms, a point is not simply notional, or purely geometric, but rather
the smallest mark a painter can make, and a contour is the finest line a
painter can draw. When he wrote this way Alberti was fully in the
tradition of classical and medieval optics.
From its beginnings, optics was regarded as a special, limited case of
an example of what in the Middle Ages came to be called a subalternate
geometry, or a middle science. Whatever they might be thought to be in
themselves, the “lines” of optics were physical; geometry itself was
“pure”, general and intellectual in contrast to optics. Simply put,
sight is not primarily geometric, it is a physical interaction of light
with the organ of vision, an interaction of surfaces that can be
described and explained in geometric terms, leaving aside the questions
of just what sort of thing rays of light might be, or just how the eye
If seeing is a physical interaction, it must be thought about in very
different terms. The Stoics, for example, compared the visual angle to a
blind man feeling his way along a path with a pair of sticks, vividly
suggesting that vision is fundamentally related to the sense of touch,
even to feeling. Leonardo da Vinci performed a simple demonstration: if
vision is adequately described geometrically, then if I put my finger in
front of my eye, the apex of the visual angle should be cut off and I
should be able to see nothing. Since I do see something, light,
the eye and their interaction must also be much more complex. Leonardo
developed linear perspective together with what he called the
perspective of disappearance, not just diminution in size but loss of
distinctness of color and detail, more properly and simply physical
limits of vision.
We have seen enough to put together a fairly simple intellectual
historical narrative. In Classical science, an idea like “precinct” was
expanded in such a way as to make the conscious individual – in
principle any individual – the center of a circle nested in the great
living circles of the cosmos itself. The horizon circle, as the example
of Heidegger at the beginning of the paper shows, retains its classical
configuration to a remarkable degree, perhaps much as the ego has
remained at the center of Western languages. The concentric cosmic
circles validating the original conception have of course dissolved, but
the metaphor of the horizon circle persists, together with
“perspective”, in a host of metaphors from phenomenology to archaeology
to culture to identity.
Through all of this, the center, the individual and subject as the locus
of distinctively human experience, life and death, has survived, if not
without continual challenge and redefinition. The second part of the
title of this paper, infinities without end, was meant to indicate the
numberless possible human spaces, times, and horizons, and also to
indicate the value these absolute particularities should have.
The first version of this paper was written for a conference on
the concept of the horizon organized by Professor Aron Vinegar
at Ohio State University. I am grateful to Professor Vinegar for
his invitation and for the stimulating discussions to which the
Heidegger, M., Being and Time, tr. John Macquarrie and E.
Robinson, New York and Evanston, 1962, p. 1.
Gadamer, H.- G., Truth and Method, New York, 1975, p.
269-74. Gadamer especially associates the concept of horizon
with Nietzsche and Husserl, who used it “to characterize the way
in which thought is tied to its finite determination”.
Summers, D., Real Spaces. World Art History and the Rise of
Western Modernism, London, 2003, p. 257-9.
Aristotle, Meteorology, 365a30; the horizon similarly
defined is also a basic part of Aristotle’s geometric discussion
of the rainbow, (ibid. 375b16-377a28), which provided the basis
for subsequent arguments; see for example the early 14th-century
Theodoric of Freiburg, De iride, in A Source Book in
Medieval Science, ed. E. Grant, Cambridge, Mass., 1974, p.
435-441. For Aristotle’s arguments for the sphericity of the
earth, see De caelo, 296a14-298b21.
Macrobius, Saturnalia, 7. 14. 15; ed. I. Willis, Leipzig,
1970, p. 450.
Macrobius, Commentarii in Somnium Scipionis, 1. 15.
15-19; ed. I. Willis, Leipzig, 1970, p. 63-4. I have mostly
followed the translation in Macrobius, Commentary on the
Dream of Scipio, tr. W. H. Stahl, New York, 1990, p. 151-2.
Stahl provides a number of other references to late antique and
On uprightness, see Summers, D., Michelangelo and the
Language of Art, Princeton, 1981, p. 576, n. 22.
A Sourcebook in Medieval Science, p. 448. Sacrobosco
defines the horizon as “a circle dividing the lower hemisphere
[earth] from the upper [sky], whence it is called “horizon”,
that is, “limiter of vision”; he also gives an absolute
definition of the “rational” horizon, which he calls “right”;
those at the equator (if, he wonders, anyone may live in such
heat) will define a circle on the globe passing through its
center and coinciding with the poles. See also L. Thorndike,
The Sphere of Giovanni Sacrobosco and its Commentators,
Chicago, 1949; and L. S. Dixon, “Giovanni di Paolo’s Cosmology”,
Art Bulletin, 67, 1985, p. 604-13.
 Trésor de la Langue Française.
de la langue du XIXe et du XXe siècle (1789-1960), Paris,
1981, 9, p. 920.
Chaucer, G., Troilus and Criseyde, V, 276; ed. S.
A. Barney, New York-London, 2006, p. 327.
Lorenzo de’ Medici, Opere, ed. Simioni, Bari, 1913, I, p.
Leonardo on Painting. An Anthology of Writings by Leonardo
da Vinci with a Selection of Documents relating to his Career as
an Artist, ed. M. Kemp, New Haven-London, 1989, p. 217-218.
A. Lobato, “Anima quasi Horizon et Confinium”, in L’Anima
nell’ antropologia di S. Tommaso d’Aquino. Atti del Congresso
dell Societa Internazionale S. Tommaso d’Aquino (SITA),Roma,
2-5 Gennaio, ed. A. Lobato, Milan, 1987, p. 59.
D. Summers, “The Heritage of Agatharcus: on Naturalism and
Theatre in European Painting”, in The Beholder. The
Experience of Art in Early Modern Europe, ed. T. Frangenberg
and R. Williams, Aldershot-Burlington, 2006, p. 9-35.
D. Summers, Vision, Reflection and Desire in Western
Painting, Chapel Hill, 2007, Chapter 2.
L. B. Alberti, On Painting and On Sculpture. The Latin Texts
of De Pictura and De Statua, tr. C. Grayson, London,
1972, p. 56-7.
D. Summers, Real Spaces, Chapter 7.
D. Summers, Vision, Imagination, and Desire, Afterword.
Alberti, On Painting, p. 36-7.
Aristotle, Physics, 194a.
D. Summers, Vision, Reflection, and Desire, Afterword.